A catalytic apparatus for purifying the exhaust gas is arranged in the engine exhaust system. A catalyst, such as a noble metal catalyst, carried on the catalytic apparatus sinters and deteriorates when it is exposed to excessive oxygen at a high temperature.
In engine deceleration, a fuel-cut is usually carried out. However, if a fuel-cut is carried out when a temperature of the catalyst is high, the deterioration of catalyst is caused by the exhaust gas in a lean condition as the mentioned above. Accordingly, it is suggested that, when the temperature of the catalyst is high, a fuel-cut is prohibited in an engine deceleration (refer to, for example, Japanese Unexamined Patent Publications Nos. 10-252532, 2001-59444, 10-280990, 11-107825, and 10-248114.)
In the above background art, when a fuel-cut is prohibited, the engine is operated in a condition in which an amount of intake air is minimized such that the engine is not stopped. However, in this case, an engine-brake becomes insufficient in comparison with a case where a fuel-cut is carried, and thus a good vehicle deceleration cannot be realized.